High-Pressure Vibrational and Structural Properties of Ni3V2O8 and Co3V2O8 up to 20 GPa

The vibrational and structural behaviors of Ni3V2O8 and Co3V2O8 orthovanadates have been studied up to around 20 GPa by means of X-ray diffraction, Raman spectra, and theoretical simulations. Both materials crystallize in an orthorhombic Kagomé staircase structure (space group: Cmca) at ambient conditions, and no phase transition was found in the whole pressure range. In order to identify the symmetry of the detected Raman-active modes under high pressure, single crystal samples of those materials were used in a polarized Raman and infrared setup. Moreover, high-pressure powder X-ray diffraction measurements were performed for Co3V2O8, and the results confirmed the structure stability also obtained by other diagnostic techniques. From this XRD analysis, the anisotropic compressibilities of all axes were calculated and the unit-cell volume vs pressure was fitted by a Birch–Murnaghan equation of state, obtaining a bulk modulus of 122 GPa.


INTRODUCTION
−10 These qualities make them desirable materials for industrial applications.Regarding the samples studied in this work, Ni and Co orthovanadates are mainly used in nanostructured systems.Both have been investigated as catalysts in the water splitting process, 11,12 as electrodes in portable power sources, 13,14 in the potential improvement of electrochemical energy storage, 15,16 in nitrogen fixation, 17 and even in glucose detection. 18he so-called Kagome-staircase orthorhombic structure of Ni 3 V 2 O 8 and Co 3 V 2 O 8 (space group: Cmca, No. 64) is formed by corrugated layers in the [010] direction of edge-sharing MO 6 octahedra interconnected with VO 4 tetrahedra (see Figure 1).Both compounds have four formulas per unit cell (Z = 4).The lattice parameters for Ni  1 It is worth mentioning that a similar polyhedral coordination is also found in metavanadates (MV 2 O 6 ) 19 and pyrovanadates (M 2 V 2 O 7 ). 20n recent years, the high pressure (HP) community has also put the focus on this family of compounds, which have demonstrated a variety of remarkable physical behaviors under pressure.X-ray diffraction (XRD) and Raman methods were used to study Mn 3 V 2 O 8 in its orthorhombic low-temperature structure; an irreversible phase transition at 10 GPa was discovered, but the new phase has not been identified yet. 21In contrast, it has been demonstrated that Zn, Ni, and Mg orthovanadates are stable up to 15, 22  23, 23 and 25.7 GPa, 24 respectively.With different structures but the same stoichiometry, Ca and Sr orthovanadates were found to undergo different phase transitions at 9.7(1) GPa 25 and 13.8 GPa, 26 respectively.Alternatively, it was reported that triclinic Cu 3 V 2 O 8 decomposes into CuO and V 2 O 5 at 1. 35 GPa. 27ote that the structural properties of Ni 3 V 2 O 8 were recently investigated by HP powder XRD by some of the authors of the present study. 24To compare with Co 3 V 2 O 8 , the data from that work are included in the current investigation.
We continue the research in orthovanadates within this paper by reporting for the first time the changes in the vibrational modes of Ni 3 V 2 O 8 and Co 3 V 2 O 8 under HP from both experiments and density functional theory (DFT) calculations.As a previous step, polarized Raman and infrared (IR) measurements are used to properly identify the symmetry of the active modes and match them with the simulation results under ambient conditions.We also present the first HP XRD analyses of Co 3 V 2 O 8 .As it is situated in the periodic table between Mn (which undergoes a phase transition at 10 GPa 21 ) and Ni (which remains stable up to 23 GPa 23 ), it is of great interest to find out what structural changes occur under pressure.The experimental data are also supported by the corresponding DFT calculations.We determined the bulk modulus and anisotropic compressibility of this compound from the structural information we have collected.Finally, we make use of all the results obtained to compare the pressure behavior of both orthovanadates.

Experimental Details.
The orientation of the single crystals was carried out by using a Bruker D8 Venture diffractometer.IR spectra at ambient conditions were collected with an FTIR Bruker IFS125 HR spectrometer using a Globar light source, KBr beam splitter, and MCT detector (cut at 600 cm −1 ).Raman spectra were acquired in the backscattering geometry using a 632.8 nm He−Ne laser, a Jobin Yvon spectrometer combined with a thermoelectric-cooled multichannel charge-coupled device (CCD) detector with a spectral resolution of 2 cm −1 , and a Semrock low-pass RazorEdge filter.A low laser power of approximately 2 mW before the diamond anvil cell (DAC) was necessary to avoid overheating the sample and wavenumber shifting.Polarizer filters were added to the Raman setup for the single crystal measurements.HP Raman measurements were performed using a DAC and a 16:3:1 methanol−ethanol−water mixture as the pressuretransmitting medium (PTM). 30The peak profile fit was achieved using a Pseudo-Voight peak profile in MATLAB software. 31The pressure gauge was determined using ruby luminescence. 32P powder XRD measurements on Co 3 V 2 O 8 were performed at the MSPD beamline of the ALBA synchrotron 33 using a monochromatic beam with a wavelength of 0.4246 Å.The beam was focused down to a spot with a full width at halfmaximum (fwhm) of 20 μm × 20 μm.A Rayonix CCD detector was used to collect XRD patterns with a sample-todetector distance of 340 mm.This sample−detector distance was required to achieve a correct angular resolution, which limited our 2θ range to around 13°.The pressure was determined using the XRD reflections and the equation of state (EOS) of Cu 34 with a precision of ±0.1 GPa.The PTM used for these experiments was a 4:1 methanol−ethanol (ME) mixture.The measurements thus obtained were transformed into one-dimensional patterns using the DIOPTAS suite, 35 and Le Bail fittings were achieved with PowderCell. 36.3.Ab Initio Density-Functional Theory Calculations.Ab initio calculations were performed within the framework of density functional theory (DFT) 37 with the Vienna ab initio Simulation Package (VASP). 38,39The projector augmentedwave (PAW) method 40,41 was employed.To ensure accurate converged results, the plane-wave kinetic cutoff was extended up to 650 and 540 eV for Ni 3 V 2 O 8 and Co 3 V 2 O 8 , respectively.The integrations over the Brillouin zone (BZ) were carried out with a k-special point sampling grid of 6 × 6 × 4.After testing different functionals to decide which was the most accurate for each compound, the exchange-correlation energy was described by means of the generalized gradient approximation (GGA) with the Armiento and Mattsson (AM05) prescription 42,43 for Ni 3 V 2 O 8 and, in the case of Co 3 V 2 O 8 , the Perdew−Burke−Ernzerhof (PBE) functional for solids. 44,45To properly treat the strongly correlated states, the DFT + U method of Duradev et al. 46 was employed.This method utilizes a single parameter, U eff = U − J, where U and J are the effective on-site Coulomb and exchange parameters, respectively.The values used for U eff 47 were 6.2 eV for Ni, 3.25 eV for V, and 3.32 eV for Co.In both compounds, the ferromagnetic configuration was found to be lower in energy.
The unit cell parameters and atomic positions were fully optimized to obtain, at selected volumes, the relaxed structure.For the optimization, the criteria used were as follows: the forces on the atoms were less than 3 meV/Å, and the deviations of the stress tensors from a diagonal hydrostatic form were lower than 0.1 GPa.Our ab initio calculations provide a data set of volumes, energies, and pressures (from the stress tensor) that are fitted with a Birch−Murnaghan equation of state 48 to obtain the theoretical equilibrium volume, the bulk modulus, and the pressure derivatives.
Lattice-dynamic calculations of the phonon modes were carried out at the zone center (Γ point) of the BZ with the The Journal of Physical Chemistry C direct force-constant approach provided by Phonopy. 49These calculations provide the frequency of the normal modes, their symmetry, and their polarization vectors.This allows the identification of the irreducible representations and character of the phonon modes at the Γ-point.To include the polarization induced by atomic displacements and the generated macroscopic electric field producing the LO/TO splitting, the nonanalytical term corrections were added using a 2 × 2 × 2 supercell, with the Born effective charges and the dielectric tensor as described in the Phonopy package.Both Ni and Co orthovanadates present the same crystalline structure, 1 whose symmetry is described by the Cmca space group.There are two molecules in the primitive unit cell, giving rise to seventy-eight vibrational modes.Point group mmm classifies the symmetry at the zone center as follows 50 : Even (gerade) modes (A g , B 1g , B 2g , and B 3g ) are Raman active.Ni/Co atoms located at inversion centers (those at the 4a Wyckoff position) remain at rest.One of each of the B 1u , B 2u , and B 3u modes corresponds to acoustic modes.The rest are IR active modes with the exception of A u modes, which are silent.All these modes have been individually labeled in Tables 1 (IR active) and 4 (Raman active).The calculated atomic motions of all vibrational modes are represented in Tables S1,  S2, and S3.Wavenumber (ω 0 ) is expressed in cm −1 and pressure (P), in GPa.
The DFT-calculated ω 0 has a related uncertainty of ±5%.

The Journal of Physical Chemistry C
The modes with the largest wavenumbers are related to the internal modes of the VO 4 tetrahedra.Taking a closer look into some of the representative modes (referring to the wavenumbers of Co 3 V 2 O 8 ), it can be seen that A g 9 (Figure 2) and B 1u 12 are V−O bond stretching modes.Both have very similar calculated frequencies (789 and 770 cm −1 , respectively), because their vibration pattern is very similar, but the inversion center makes the equivalent V and O movement through this point in phase or in phase opposition.Other examples of phonons related to the internal movement of the tetrahedra are the B 3g 9 , Figure 2, and B 2u 10 modes (670 and 642 cm −1 , respectively).Their vibration pattern includes bending of V−O bonds.From 640 to 440 cm −1 , there is a frequency gap that divides internal from external modes.The more energetic mode with a relevant Co amplitude is the A u 7 mode at 460 cm −1 .The amplitude is, however, not large enough to be appreciated in Table S3.It is remarkable that internal modes have similar frequencies in Co and Ni compounds (a difference of less than 4%).In external modes where the M amplitude is relevant, the wavenumber differences are more pronounced.The mode with the largest Co amplitude is the B 1u 2 mode.The wavenumbers in Co and Ni compounds differ by 16% (124 and 144 cm −1 , respectively).The mode B 3u 2 (144 cm −1 in the Co compound) constitutes an example of rotation of the VO 4 tetrahedron, in this case having a V−O bond as an axis, Figure 2. The mode also involves a significant shift of the Co atoms.Finally, the low wavenumber mode A g 1 (111 cm −1 , Figure 2) represents a mode where atoms in a plane roughly defined by z ≅ 0.25 vibrate in phase opposition respect to atoms in a z ≅ 0.75 plane, while atoms near z = 0 and 0.5 remain static.The large mass involved implies low frequency mode.Other similar modes are B 1u 2 (124 cm −1 ) and B 1g 1 (121 cm −1 ).3.2.Ambient Conditions for Infrared Spectroscopy (Ni 3 V 2 O 8 and Co 3 V 2 O 8 ).IR modes were identified using polarization and considering that B 1u , B 2u , and B 3u modes transform as z, y, and x, respectively.The ab initio calculated IR active modes, including the transversal optic (TO) and longitudinal optic (LO) splittings and the corresponding pressure coefficients, are reported in Table 1.Furthermore, in Table 2, using the theoretical IR phonon wavenumbers and the simulated static dielectric constants (ε 0 ), the infinite dielectric constants (ε ∞ ) were calculated using the Lyddane-Sachs Teller relation. 51he growth conditions of the samples favored the formation of single crystals with the largest surface perpendicular to the yaxis.The measurements were taken on the [010] surface.The spectral region for the present IR measurements covered from 600 to 4500 cm −1 .Therefore, only the three highest frequency B 1u modes and the last B 3u for both Ni 3 V 2 O 8 and Co 3 V 2 O 8 single crystals were accessible.These modes were selected using polarizers, as represented in Figure 3.The dielectric constant was modeled using the following relation: where ω TO , ω LO , γ TO , and γ LO are the frequencies and damping factors of the transverse and longitudinal optic modes, respectively. 52Using eq 1, the reflectivity of the material, ( 1)/( 1) 2 , can be obtained, and then, the total reflectance of the sample can be calculated, considering that the body with parallel surfaces undergoes consecutive internal reflections, as follows: (1 ) where α is the absorption coefficient.Equation 2 was used to fit the experimental data in Figure 3.In the spectral region where the sample is transparent, this expression simplifies to The criteria chosen for data normalization are based on the reflectance (3) at 4500 cm −1 , where the sample is transparent and the reflectance is estimated using the calculated static dielectric constant from Table 2.
The experimentally determined IR modes are gathered along with the calculated modes in Table 3.It is noticeable that both experimental and theoretical values are in good agreement, including the TO-LO splitting values.5) a γ 0 is the damping factor of the fitting in cm −1 , and ω 0 is expressed in cm −1 .The DFT-calculated ω 0 has a related uncertainty of ±5%.i k j j j j j j j j j y { z z z z z z z z z i k j j j j j j j j j y { z z z z z z z z z i k j j j j j j j j j y { z z z z z z z z z i k j j j j j j j j j y The resulting selection rules provide the advantage of being able to measure the modes separately, always in the backscattering configuration, employing the previously oriented single crystals.Additionally, it must be noted that A g and B 1g /B 2g /B 3g modes are allowed when the backscattered signal from the single crystal sample is polarized parallel or perpendicular to the polarization of the incident laser, respectively.On the other hand, B 1g /B 2g /B 3g modes can only be measured if the surface of incidence is oriented in the crystallographic c/b/a-axis (hereon referred to as z/y/x).Depending on the specimen, other smaller surfaces different from [010] were also available.In the case of Ni 3 V 2 O 8 , a single crystal with a small [001] face was measured.In addition, a third perpendicular surface could be measured, starting from the [010] plane and tilting the DAC 53°with respect to the zaxis (from now on called the ξ orientation; see Figure 4), which yielded a spectrum containing B 1g and B 3g modes.In the case of Co 3 V 2 O 8 , only the [010] and [001] surfaces were available.The Raman characterization of both compounds at room temperature was completed with a powder spectrum.
The complete symmetry phonon assignment for Ni 3 V 2 O 8 is shown in Figure 4.All 10 A g modes were found using coincident polarization in all 3 orientations of the crystal (except for A g 2 , which was found only in the ξ orientation).a ω 0 is expressed in cm −1 , and P, in GPa.The DFT-calculated ω 0 has a related uncertainty of ±5%.Discrepancies in symmetry assignation with Kesari et al. 53 are included in its column.

The Journal of Physical Chemistry C
Using crossed polarization, the B 1g modes were identified when inciding along the z-axis (6 out of 8), B 2g modes, with yincidence (6 out of 7), and a mixture of B 1g and B 3g , in the ξaxis (7 out of the 11 total B 3g ).There was no polarization leakage in any of the spectra, except for the most intense mode, A g 10 , which was also measured in crossed polarization at orientations z and ξ.Thus, a total of 29 modes of the 36 Raman-active modes are reported.Kesari et al. found 30 modes experimentally and performed DFT calculations. 53Overall, this work is in good agreement with this study, except that the symmetry of some nearby modes are not assigned in the same way (see B 1g  4), and not all the modes detected are the same.Combining both works, there are only 3 modes not detected experimentally.The analogue study for Co 3 V 2 O 8 can be seen in Figure 5, which was less successful in comparison with the Ni compound due to its higher absorption of the excitation laser, giving rise to a sizably lower Raman signal.For this crystal, the parallel polarization measurements showed 9 of the total 10 A g modes.Using crossed polarization, 5 B 1g modes were detected with z incidence and 2 B 2g modes, with y incidence.In all cases, small leaked contributions to A g modes were found.Finally, all peaks from the polarized measurements were compared with those obtained from the powder sample, which allowed us to detect 2 extra modes belonging to the B 3g symmetry.The total amount of detected zone-center modes for the Co vanadate is 18 modes of the 36 available.Seo et al. were able to measure 8 modes of this compound, 54     The Journal of Physical Chemistry C spectra in Figures 6 and 7, respectively.Pressure coefficients under ambient conditions are presented in Table 4.The pressure coefficients were fitted using the spectra obtained near ambient conditions, where the dependence on pressure is linear.As found in previous HP XRD studies 23 for Ni 3 V 2 O 8 , this compound does not undergo any nonisostructural phase transition in the covered pressure range.Now, this statement can also be applied to Co 3 V 2 O 8 .
The pressure dependence of the calculated and experimentally measured phonon wavenumbers is shown in Figure 8 for Ni 3 V 2 O 8 and in Figure 9 for Co 3 V 2 O 8 .It can be seen that all of the observed modes, except the A g 1 mode, upshift with increasing pressure.In Co 3 V 2 O 8 , the A g 8 and B 3g 9 modes were no longer differentiated out of the background because of signal attenuation as pressure increased.The experimental values of these coefficients are broadly in good agreement with those obtained in the ab initio calculations.The calculated lines in Figures 8 and 9 run parallel to the experimental points with the calculated lines generally shifted by less than 5% with respect to the measured data.Only a single crossover is observed experimentally between B 2g 6 and A g 7 in Ni 3 V 2 O 8 , which is well reproduced by the DFT calculations.All data sets collected on decompression follow the same behavior as upstroke measurements.When comparing both orthovanadates, the first dissimilarity observed is that, in spite of the larger mass of Ni, all modes in Co 3 V 2 O 8 are slightly lower in wavelength (approximately 10 cm −1 ), while high-pressure events, such as the mode crossover, occur earlier in pressure for Ni 3 V 2 O 8 (see A g 6 -B 1g 7 , A g 3 -B 1g 4 , or A g 6 -B 3g 7 in Figures 8 and 9).  10 for selected pressures.The patterns shown correspond to positions of the DAC where there was no Cu signal.This compound does not exhibit any phase transition in the mentioned pressure region, as was also published for Ni 3 V 2 O 8 . 24ubsequently, the pressure dependence of the unit-cell parameters and corresponding volume of the orthorhombic structure of Co 3 V 2 O 8 is reported in Figure 11, using the results from the Le Bail fits 55 and peak indexation with UNITCELL. 56t 10.5(1) GPa, a slight change in the evolution of all three unit-cell axes was noticed.This fact coincides with the end of the hydrostatic region of the ME pressure-transmitting media, 27 which is probably the reason that the linear compressibility of each axis is reduced.This nonhydrostatic effect led us to report two separate equations of state (EOSs), one up to the hydrostatic limit of ME (9.3(1) GPa) and another up to the maximum pressure (20.0(1)GPa).Thus, the unit-cell volume was fitted using a third-order Birch− Murnaghan EOS 48 employing EosFit7 software. 57The third order of the EOS was determined from the Eulerian strainnormalized pressure dependence of the data. 58All EOS parameters are reported in Table 5, along with literature ones for other Kagome-staircase orthovanadates.The unit-cell parameters obtained by DFT calculations differ from the  The Journal of Physical Chemistry C experimental parameters by approximately 1% in terms of absolute value.Furthermore, the bulk moduli obtained in the EOS for both calculations (129.2(7)GPa) and experiments up to 9.3(1) GPa (127.4(4)GPa) are in good agreement.Comparing these results with the bulk modulus reported for Ni 3 V 2 O 8 , 24 it can be noticed that Co orthovanadate is more compressible than Ni orthovanadate.For this comparison, the two bulk moduli obtained by a second order EOS and under hydrostatic conditions were used, whose values are 122(4) and 143(3) GPa for Co and Ni vanadates, respectively (see Table 5).This fact agrees with the observations reported in the HP Raman section (3.4), where it was concluded that Ni 3 V 2 O 8 behaves as a pressurized version of Co 3 V 2 O 8 .Overall, Ni and Co vanadates show bulk moduli within the range of all other Kagome-staircase orthovanadates, with Mg 3 V 2 O 8 being the highest (152(4) GPa) 23 and Mn 3 V 2 O 8 , the lowest (106(3) GPa) 21 to date.
From the reported unit-cell parameters, the linear isothermal compressibility was calculated for all axes of the orthorhombic structure: = ( ) The region used for the fits is from 0.0(1) to 9.3(1) GPa to guarantee that only hydrostatic data are used.When these compressibilities are compared with the experimentally obtained ones for Ni 3 V 2 O 8 23 and simulated for other orthovanadates, 59 it can be clearly appreciated that they follow the same behavior followed for this family of compounds, but the b-axis of Co 3 V 2 O 8 is slightly more compressible.Once more, this can be related to the "compressed" structure of Ni 3 V 2 O 8 indicated in Section 3.4, since the b-axis is mainly influenced by the layers of CoO 6 octahedra (see Figure 1), which are more compressible than the NiO 6 octahedra.The DFT-calculated change in bond distances within the covered pressure range can be seen in Figures S1 and S2 for both compounds.

CONCLUSIONS
High-pressure vibrational studies were performed for Ni 3 V 2 O 8 and Co 3 V 2 O 8 powders up to 19.5(1) and 20.4(1) GPa, respectively, and no phase transition was found.Polarized Raman and infrared measurements on single crystals were used to separate and identify the symmetry of the vibrational modes for both compounds under ambient conditions.Ab initio DFT calculations are reported to confirm the symmetry, ambient pressure wavenumber value, and pressure coefficients of all the experimental modes found (24 for Ni 3 V 2 O 8 and 17 for Co 3 V 2 O 8 out of the 36 Raman active modes).Although both Ni and Co orthovanadates present a similar vibrational behavior under pressure, it is found that Ni 3 V 2 O 8 exhibits a more compact version of the structure.HP angle dispersive

The Journal of Physical Chemistry C
powder XRD analysis up to 20.0(1) GPa was also performed for Co 3 V 2 O 8 .Anisotropic compressibility and EOS parameters (including bulk moduli) are obtained from both the experimental results and the DFT calculations.Excellent agreement is found between the two sets of data.

Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.

Figure 1 .
Figure 1.Crystal structure of the M 3 V 2 O 8 orthovanadate Kagomestaircase family.Atoms and unit-cell axis are labeled on the left.MO 6 octahedra are shown in blue, and VO 4 tetrahedra are shown in green.

Figure 2 .
Figure 2. Representative vibrational modes of M 3 V 2 O 8 (M = Ni, Co) using the primitive unit cell.M is in pink, V in gray, and O in red.Blue arrows represent the key motion, while blue dots represent key atoms in still positions.

Figure 3 .
Figure 3. Experimental infrared reflectivity (dots) using 3 different incident polarizations.Solid lines represent the best fit 54 for each set of data.

Figure 4 .
Figure 4. Symmetry assignment of the Raman modes of Ni 3 V 2 O 8 at ambient conditions.The vertical ticks represent the DFT calculation results, matching in color with the corresponding symmetry.The incidence direction ξ of the tilted sample is sketched.If any magnification or reduction factor is applied to the data region, it is labeled next to it.
obtaining similar frequency values compared with this work.All of these mode identifications are supported by ab initio computations, showing satisfactory experiment−simulation agreement.The ambient pressure wavelength values of the vibrational modes for Ni 3 V 2 O 8 and Co 3 V 2 O 8 , along with the calculated and literature values, are shown in Table 4. 3.4.High-Pressure Raman Spectroscopy (Ni 3 V 2 O 8 and Co 3 V 2 O 8 ).In the present powder vibrational HP studies, 24 modes for Ni 3 V 2 O 8 are monitored up to 19.5(1) GPa and 14 modes for Co 3 V 2 O 8 , up to 20.4(1) GPa, as shown for selected

Figure 5 .
Figure 5. Symmetry assignment of the Raman modes of Co 3 V 2 O 8 at ambient conditions.The vertical ticks represent the DFT calculation results, matching in color with the corresponding symmetry.The magnification of the low wavenumber region is 20×.

Figure 6 .
Figure 6.Raman spectra corresponding to Ni 3 V 2 O 8 at selected pressures.The symmetry modes are assigned colors in the first pattern.Numbers next to the spectra indicate pressure in GPa.Downstroke data are marked with a "d".Magnification of the first region is shown in the top left corner.

Figure 7 .
Figure 7. Raman spectra corresponding to Co 3 V 2 O 8 at selected pressures.The symmetry modes are assigned colors in the first pattern.Numbers next to the spectra indicate pressure in GPa.Downstroke data are marked with a "d".Magnification of the first region is shown in the top left corner.
These observations suggest that Ni 3 V 2 O 8 behaves as a pressurized version of Co 3 V 2 O 8 .3.5.High-Pressure X-ray Diffraction (Co 3 V 2 O 8 ).Using the XRD patterns collected for powder Co 3 V 2 O 8 under HP, the orthorhombic structure (space group Cmca, number 64) was fitted from 0.0(1) to 20.0(1) GPa.Le Bail refinement 55 results are shown in Figure

Figure 8 .
Figure 8. Pressure dependence of the Raman modes of Ni 3 V 2 O 8 .The symmetry modes are assigned with colors on the right, matching the end of the solid line in the figure.

Figure 9 .
Figure 9. Pressure dependence of the Raman modes of Co 3 V 2 O 8 .The symmetry modes are assigned with colors on the right, matching the end of the solid line in the figure.

Figure 10 .
Figure 10.XRD patterns at selected pressures (black dots) of Co 3 V 2 O 8 .Le Bail fits and residuals are shown with blue and red lines, respectively.Ticks indicate the Bragg peaks for the corresponding structural phase.Pressures are indicated in the figure.The top trace corresponds to the last experiment made during decompression.

Figure 11 .
Figure 11.Pressure dependence of the unit-cell parameters (top) and volume (bottom) of Co 3 V 2 O 8 .Black symbols represent experimental measurements, and red lines are DFT calculations.Full circles represent upward pressure, while empty triangles release pressure data.The solid black line and dashed black line are the Birch− Murnaghan EOS fitting of the experimental unit-cell volume up to 9.7 and 20 GPa, respectively.
3 V 2 O 8 / Co 3 V 2 O 8 were synthesized by means of a solid-state reaction starting with NiO/CoO (99.995% purity) and V 2 O 5 (99.9% purity).The precursors were obtained from Alfa Aesar.An Al 2 O 3 crucible was used to heat the mixed reagents in air at 800 °C for 16 h.The product was then ground and pressed into a pellet, which was sintered at 900 °C for an additional 16 h.For the single crystal preparation, Ni 3 V 2 O 8 /Co 3 V 2 O 8 powders were prepared at 900 °C for 40 h by a standard/ high-temperature solid-state reaction method using NiC 2 O 4 • 2H 2 O/CoC 2 O 4 •2H 2 O and V 2 O 5 as the reagents with a molar ratio of 3:1.The crystal growth was performed in an electric furnace, where Ni 3 V 2 O 8 /Co 3 V 2 O 8 powder samples and flux V 2 O 5 and SrCO 3 (also BaCO 3 for Co 3 V 2 O 8 ) were melted homogeneously in an alumina crucible at 1000 °C and kept at 1000 °C for 10 h, cooled slowly to 800 °C/700 °C at a rate of 0.5 °C/h (making constant temperature stops several times in between), and finally cooled to room temperature at a rate of approximately 100 °C/h.The final Ni yellow crystals (∼3 × 3 × 0.5 mm 3 )/Co dark blue crystals (∼4 × 4 × 1 mm 3 ) were obtained by mechanical separation from the crucible.A detailed growth procedure is described in ref 28 for Ni 3 V 2 O 8 and in ref 29 for Co 3 V 2 O 8 .

Table 1 .
Ab Initio Calculated IR Modes under Ambient Conditions a

Table 2 .
Ab Initio Calculated Diagonal Components of the Static and Infinite Dielectric Constants of Ni 3 V 2 O 8 and Co 3 V 2 O 8 in Ambient Conditions

Table 3 .
Theoretical and Experimental Zone-Center IR Modes for Ni 3 V 2 O 8 and Co 3 V 2 O 8

Table 4 .
Raman Modes, Wavenumbers, and Pressure Coefficients Corresponding to the Zone-Center Active Raman Modes under Ambient Conditions for Ni 3 V 2 O 8 and Co 3 V 2 O 8